In the speech enhancement setting, we have an input noisy signal \(\tilde{\textbf {x}}\)  that has to be cleaned to obtain the enhanced signal \(\hat{\textbf {x}}\) . SEGAN decimates and expands the input signal feature-wise, through a number of strided convolutional layers with multiparametric rectified linear activations (PReLUs) [1]}. Decimation is applied until we obtain a compact representation of a few time samples \(\textbf {c}\) . This result is concatenated with the generative noise component \(\textbf {z} \sim \mathcal {N}(0, I)\) , which adds the generative stochastic behavior to the generator predictions \(\hat{\textbf {x}}\) . Decimation discourages learning a trivial identity function in the reconstruction \(\tilde{\textbf {x}}\) , and also accelerates the convolution operations when we go deeper in the decimation structure of the encoder (shorter sequence lengths involve faster processing). It also reduces the memory footprint by using shorter feature maps. The encoding process is then reversed in the decoding stage by means of transposed convolutions, followed again by PReLUs until last layer which is \(\tanh \)  to bound the output between \(-\) 1 and 1, stabilizing the adversarial process [2]}. Additionally, skip connections linking the encoder and the decoder of \(G\)  boosted stability and generated quality.The enhanced output signal is thus defined at the output of the decoder as \(\hat{\textbf {x}} = G(\textbf {z},\tilde{\textbf {x}})\) .
